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PreprintarXiv licencearXiv

Alexandrov-Type Rigidity for Minimal Capillary Hypersurfaces on Rotational Supports

  • Caiyan Li
  • Chao Xia
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Abstract

In this paper, we prove that, under suitable conditions on the generating profile, every connected, compact embedded minimal capillary hypersurface supported on a one-ended rotational hypersurface in the Euclidean space is a horizontal slice. We also construct a smooth one-ended rotational support carrying a non-horizontal planar capillary n-ball, showing that the main slope condition cannot in general be omitted. For obtuse contact angles, we further obtain a catenoid-band classification under a reverse profile inequality.

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Cite

BibTeXRIS
BibTeX
@misc{li2026alexandrovtype,
  title = {{Alexandrov-Type Rigidity for Minimal Capillary Hypersurfaces on Rotational Supports}},
  author = {Caiyan Li and Chao Xia},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10318},
  eprint = {2609.10318},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10318},
}
RIS
TY  - UNPB
TI  - Alexandrov-Type Rigidity for Minimal Capillary Hypersurfaces on Rotational Supports
AU  - Caiyan Li
AU  - Chao Xia
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10318
UR  - https://arxiv.org/abs/2609.10318
AB  - In this paper, we prove that, under suitable conditions on the generating profile, every connected, compact embedded minimal capillary hypersurface supported on a one-ended rotational hypersurface in the Euclidean space is a horizontal slice. We also construct a smooth one-ended rotational support carrying a non-horizontal planar capillary n-ball, showing that the main slope condition cannot in general be omitted. For obtuse contact angles, we further obtain a catenoid-band classification under a reverse profile inequality.
ER  -